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Ideas for 'Mathematical Methods in Philosophy', '06: Romans' and 'Higher-Order Logic'

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5 ideas

5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models

18744

Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

10292

Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]

10590

Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]

10296

The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]

10297

The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]